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Rational defect groups and 2-rational characters
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David Gluck
Published/Copyright:
December 1, 2010
Abstract
Let D be a defect group of a 2-block B of a finite group G. We conjecture that if D is a rational group and D′ ⩽ Z(D), then the values of all χ ∈ Irr(B) lie in a cyclotomic field ℚm, for some odd integer m. We prove the conjecture when G is solvable or |D| = 8. Examples show that the condition D′ ⩽ Z(D) cannot be relaxed.
Received: 2010-03-26
Revised: 2010-07-06
Published Online: 2010-12-01
Published in Print: 2011-May
© de Gruyter 2011
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Articles in the same Issue
- On Lyndon's equation in some Λ-free groups and HNN extensions
- On triple factorizations of finite groups
- Approximation of automorphisms of the rationals and the random graph
- Bass–Serre theory and counting rank two amalgams
- Rational defect groups and 2-rational characters
- The imprimitive faithful complex characters of the Schur covers of the symmetric and alternating groups
- Real and strongly real classes in SLn(q)
- Real and strongly real classes in PGLn(q) and quasi-simple covers of PSLn(q)
